Flattening the Earth

First we learned the world was round. Now we’re learning how to flatten it.

For millennia, humans believed that the Earth was flat.

The Egyptians thought the Earth was a disc floating in an endless ocean, covered by a solid dome of sky. Ancient Chinese believed that the Earth was a large square under a  circular heaven. Norse myths assumed a flat planet linked to other realms by Yggdrasil, the world tree.

Then, around the 8th century CE, the idea of a spherical Earth began to propagate among scholars. 9th century Greeks tried to measure its circumference. Writers of 10th century texts, including Thomas Aquinas, often assumed the concept of a globe.

Today, it feels like a fact of reality. Grass is green, the sky is blue, and the Earth is round.

Or is it?

The Earth is not, in fact, round. That is to say, it isn’t a perfect sphere — it’s probably closer to a potato or a pear, flattened at the pole and bulged at the equator.

We call this potato a geoid, and it represents the hypothetical shape of the Earth, where gravity is the same at every point. However, you may have noticed the use of the word ‘hypothetical’ in the previous sentence. That’s because the potato’s surface coincides only with the average sea level, whereas the real world has mountains and craters and trenches and bumps.

This lack of regularity makes geo-location very complicated. So, in order to make life easier, researchers have created a base of reference called the ‘ellipsoid’ that the geographer can then superpose the true geoid onto. They basically take a simpler model, and pretend it’s the more complicated one.

When studying the Earth, a geographer has many ellipsoid models to choose from. Some ellipsoids have their surface very close to the geoid in North America, while others work better at representing Europe. The ellipsoids which have a general representation of the Earth without focusing on any area all have their centre at the centre of the Earth. Geographers generally choose one based on the focus of their study.

Ellipsoids in particular are ideal for global study, but not precise enough for local searches. For those, we’d have to turn to an altogether different solution.

Ellipsoid models can be used to superimpose a grid of coordinates on the Earth.

The grid is based on parallels and meridians. Parallels, as the name might imply, are lines that run parallel to the equator and decrease in size as they grow closer to the poles, with the largest being the equator. Meridians are perpendicular to the parallels and link the north pole to the south pole.

The most famous meridian, possibly, is the one that passes over Greenwich in England, and gives us the GMT timezone.

The coordinates tell you how far along on the grid you are: latitudes tell you the distance along the meridian, and longitude the distance along the parallel.By looking at these coordinates, you can tell exactly where you are at any given point.

As you might imagine, having this grid on the globe is extremely convenient, but having to go around with a huge ball is less so.

The solution to this problem? Maps.

If you’ve ever opened up an orange’s peel, you know that it’s very hard to do and still have it be in one piece. It’s also very hard to get it to lay perfectly flat without cutting it up. Both of these are very relevant problems for trying to represent a globe as a two-dimensional grid.

As the mathematician Leonard Euler demonstrated in 1777, there will always be empty space or wrinkle on the surface. This means just one thing for us, and you may have guessed it already: all maps are wrong!

Maps don’t represent the true world as it is, but as a cartographer has chosen to show you. This depends on his goal, of course. Will he focus on keeping the shape of the continent true? The area? The direction and distance to travel from one place to another?

In fact, the mercator map, which is the map everyone thinks of when the picture the planet and all it’s countries, was drawn half a century ago. At the time, it was considered great technological progress since navigators were able to see the world they were sailing on; They were able to navigate along lines of constant compass bearing.

That was what the creator of the Mercator map chose — direction.

But that also means that it has its weaknesses: the further an area is from the equator, the bigger it is. That’s why Africa looks way smaller than it is in reality, and the North American continent far larger Mercator’s map still have the advantage to be the best compromise of deformation. As I said earlier this deformation is due to the way we make maps and our impossibility to make them well.

There are three ways to project the spheric face of Earth on a flat paper.

The one used in the Mercator is the cylindrical method. Imagine a cylinder rolling at the surface on the Earth and printing any Earth surface features on it. Then the cylinder is cut and open to obtain a rectangular map. But the cylinder will not roll everywhere; it may touch the equator but not the extreme polar areas.

The second projection is the conical one. Imagine putting a Chinese hat on the Earth. In this case, one hemisphere will be well printed while the other one not at all. The Lambert conical projection is used in America because it best represents the northern hemisphere between 30°- 60° latitude.

The last projection is the zenithal. A flat plane is put at the top of the Earth, let’s say the pole. In this, the obtained drawing will precisely detail a small area but not the other part of Earth.

Anyone that’s ever seen a metro grid, like the famous New York subway grid, knows that maps sometimes bear no relation to the ground they represent. There may be straight lines where there should be curves. There may be angles where there should be curves.

Ultimately, whether the Earth is round or the Earth is flat,what matters is that the person looking at it knows where they are and where they want to go, and most importantly, how to get there.